Anglo-Saxon poetry is famous for its "kennings" – highly figurative compound noun constructions. That's just a fancy way of saying that kennings squash together two related nouns, so that they mean something new in a metaphorical way. The most famous kenning – the one that most English textbooks mention as their primary example – comes from "The Seafarer." It's "whale-road," which the poem uses in line 63 to describe the ocean (it also pops up in Beowulf). Many of the kennings in "The Seafarer" are often lost in translation. For example, in line 55, "heart" is actually breosthord, or "breast-treasure." The word that's translated as "breast" at line 68, hreþerlocan, literally means "spirit-locker," making this another kenning.
Another hallmark of Anglo-Saxon poetry is its alliteration. Each line is composed of two half-lines, which are bound together by alliteration – the repetition of the same sound at the beginnings of words. A line of Anglo-Saxon poetry always contains at least three, and often four or more, alliterations. (For more on this, check out "Form and Meter.")
Plus, there's always the issue of subject matter. Much Anglo-Saxon poetry contains tales of brave deeds and the warriors who do them. While "The Seafarer" doesn't have any battle sequences, you might see our speaker as a brave hero, striving against the sea to return home to his God.
Bottom line: there's no question about it, this is an Anglo-Saxon poem. Oh, the fact that it's written in Old English helps, too.